1. Field of the Invention
The present invention generally relates to a filter technique, in particular, to a method for calculating coefficients of a filter.
2. Description of Related Art
In a communication system, an equalizer of receiver is capable of eliminating interferences of received signal caused by channel, and the equalizer can be classified into an infinite impulse response (IIR) equalizer and a finite impulse response (FIR) equalizer. In terms of performance, the IIR equalizer is capable of achieving minimum mean-square error (MMSE), which is obviously superior to the FIR equalizer. However, when calculating the coefficients of the IIR equalizer, spectral factorization or other iterative algorithms such as Kalman algorithm must be used. If a non-iterative spectral factorization such as a cepstrum method is used to calculate the coefficients of the IIR equalizer, the Fourier transform with a large size must be used, and a sufficient high spectrum sampling rate is required to ensure the accuracy of the factorization. Thus the corresponding excessive high computational complexity severely inhibits the application of the cepstrum method. If an iterative algorithm is used, the time consumption and the convergence problem must be considered. Therefore, the IIR equalizer must carry out excessively computations or spend a lot of time to calculate the coefficients thereof. Moreover, in terms of the circuit design, the complexity of the IIR equalizer becomes relatively high. In addition, a transfer function of the IIR equalizer is divided into a numerator function and a denominator function. If the pole of the denominator function of the IIR equalizer is excessively close to a unit cycle on the z plane, the IIR equalizer tends to be unstable.
In contrast, since the FIR has smaller computations, lower complexity, and without the problem of instability, it still has been widely used in the equalizer of the current receiver even if the performance of FIR is significantly lower than that of the IIR.